On uniqueness theorems for the inverse problem of electrocardiography in the Sobolev spaces

We consider a mathematical model related to reconstruction of cardiac electrical activity from ECG measurements on the body surface. An application of recent developments in solving boundary value problems for elliptic and parabolic equations in Sobolev type spaces allows us to obtain uniqueness the...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Mechanik 2023-01, Vol.103 (1), p.n/a
Main Authors: Kalinin, Vitaly, Shlapunov, Alexander, Ushenin, Konstantin
Format: Article
Language:English
Subjects:
Boundary value problems
Electrocardiography
Elliptic functions
Inverse problems
Mathematical models
Numerical methods
Sobolev space
Uniqueness theorems
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Summary:We consider a mathematical model related to reconstruction of cardiac electrical activity from ECG measurements on the body surface. An application of recent developments in solving boundary value problems for elliptic and parabolic equations in Sobolev type spaces allows us to obtain uniqueness theorems for the model. The obtained results can be used as a sound basis for creating numerical methods for non‐invasive mapping of the heart. We consider a mathematical model related to reconstruction of cardiac electrical activity from ECG measurements on the body surface. An application of recent developments in solving boundary value problems for elliptic and parabolic equations in Sobolev type spaces allows us to obtain uniqueness theorems for the model. The obtained results can be used as a sound basis for creating numerical methods for non‐invasive mapping of the heart.
ISSN:0044-2267
1521-4001
DOI:10.1002/zamm.202100217